Question: $g(n) = n^{2}-2n-6$ $f(t) = -t^{3}+6t^{2}-2t+5(g(t))$ $h(t) = -6t^{2}+6t-5(f(t))$ $ g(f(2)) = {?} $
First, let's solve for the value of the inner function, $f(2)$ . Then we'll know what to plug into the outer function. $f(2) = -2^{3}+6(2^{2})+(-2)(2)+5(g(2))$ To solve for the value of $f$ , we need to solve for the value of $g(2)$ $g(2) = 2^{2}+(-2)(2)-6$ $g(2) = -6$ That means $f(2) = -2^{3}+6(2^{2})+(-2)(2)+(5)(-6)$ $f(2) = -18$ Now we know that $f(2) = -18$ . Let's solve for $g(f(2))$ , which is $g(-18)$ $g(-18) = (-18)^{2}+(-2)(-18)-6$ $g(-18) = 354$